Modern engineering analysis has led to major improvements in product design and innovation. Integrated geometric design tools, Computer Aided Design (CAD), with finite element packages are ubiquitous. Building on this success, researchers and practitioners would like to extend the application of engineering analysis to problems of existing systems, i.e. ones that were not created within a CAD system. Such domains might include forensics, reverse engineering, analysis of the natural environment, and the life sciences. An emerging area of great interest is bringing the success of engineering analysis enjoyed in product design to medicine. The goal is to be able to engineer specific medical treatments for each patient, referred to as patient-specific medicine. The common thread linking these diverse domains is that the geometry of the problem to be analyzed does not come with a ready mathematical description, as in CAD, but rather in the form of a set of discrete points. The challenge, then, is to develop an analysis-suitable description of the problem domain directly from the point set.
Currently, there exists visualization models, which are typically mesh-based, and often only represent the outer surface of the object. Their purpose is to be displayed on a graphics device, and the only requirement for these models is that they look good. There is no requirement that visualization models be anything more than realistic looking models. Hence, there is never a discussion on accuracy or comparison to known exact solutions to actual problems. It is generally easy to get a reasonable visualization model from a point set, but the resulting mesh often has serious geometric and/or topological flaws that prevent it from being usable to solve the actual equation of engineering and physics that govern the actual behavior of the object.
While visualization models have existed prior to computers and have become fairly simple to create, behavior models necessarily require a computer to properly simulate the behavior of the object. Prior to the present invention, the digitized models have required considerable amount of manual human intervention to guide the computer software to alter the visualization models into models suitable for simulation, which is explained in greater detail below. Thus, the computer graphics industry must spend a considerable amount of time and effort to develop behavior models.
Behavior models are also referred to by practitioners in the field as analysis-suitable geometry (ASG). Strictly speaking, this means that the model possesses the correct mathematical qualities to allow one to solve the actual governing equations of physics, chemistry, and biology using the models. Analysis-suitable geometries serve as visualization models, as well, so if one has an ASG, there is no need for a separate visualization model. Because one can solve the actual governing equation on an ASG, one is modeling the actual behavior of the object, not just providing a visual display or movie of how the object might look.
The significance of the present invention is in the radical reduction of time required to build an ASG from a digital point set. As an example, the inventor has built two, high-fidelity ASG models, one for a human brain, and another for the female pelvic floor. The brain was built as an ASG using the method of the present invention in about 1 minute of CPU time. Using existing technology, that same model would take roughly 4 engineers 1 year to build and cost about $1.2 million. The pelvic floor model was built in less than 10 minutes CPU time. The best model creation time by the leaders in the field for the same model is 18 months. The reason for these lengthy build times is the immense effort required to take a visualization mesh model, and fix it up to make it analysis-suitable.
An ASG model opens the door to applying engineering design techniques to patient-specific medicine. For the pelvic floor, it can be used to run virtual childbirth simulations for a pregnant woman to engineer her delivery for minimizing damage to her body and lowering risk for later life diseases. The brain can be used to model traumatic brain injury for improving design of protective gear. Unfortunately, existing methods of developing ASGs are too time consuming and costly to build for patient specific medicine, as further explained below.
One existing method for developing an ASG representation is to mesh a point set for use in finite elements, as exemplified in FIG. 1. This option includes difficulties in developing a mesh that is topologically sound, i.e. does not intersect or overlap, does not have holes or gaps, etc., can be quite difficult. In practice, an analyst often must manually assist in the meshing process. Such efforts are time-consuming and expensive in human time. Efforts have been made to automate the task of generating quality finite element meshes for complex geometry with some success. For example, generic template meshes have been mapped to patient specific geometry in order to curtail human effort [Salo, Beek, and Whyne (2013), Baghdadi, Steinman, and Ladak (2005) and Bucki, Lobos, and Payan (2010)]. Yet, simulating large deformations proves troublesome for these meshes.
Another option is to use a mesh free method. The computation of mesh free shape functions requires each point to be associated with a compact support and that the compact supports overlap, such that they cover the domain. Each point must also associate with a portion of volume. Many of the proposed methods for computing particle volume and supports rely on Voronoi diagrams or other mesh concepts. Generating such diagrams can be expensive in R3, so avoiding them is crucial in developing an automatic and efficient method. R3 is a symbol for a set of three-dimensional points that can be represented as a vector.
Another method, U.S. Pat. No. 8,854,366 B 1 to Simkins et al., teaches building an ASG from a discrete point set using a method known as the Reproducing Kernel Element Method (RKEM). The RKEM method is based on a mesh of the problem domain. The subject of the disclosure was how to develop a smooth ASG from an arbitrary point set, but the method still requires one to generate a mesh of the point set, then develop the geometric representation along with a method to help determine what the mesh should be. The Simkins patent necessitates the generation of an initial mesh, referred to as the “surface triangularization,” to generate additional points for the mesh-free representation. The current invention obviates any requirement to use an initial mesh. For the exemplary application discussed below, a voxel mesh is initially used, which is easily obtained from medical images for determining the representative volume associated with each particle (also called a mesh free node or vertex). The distinction is that the present invention does not require generating a triangularization of an arbitrary point set. The exemplary application simply utilizes the voxel mesh that is provided through the imaging. Another distinction between the current disclosure and the issued patent is that the previous method requires that any new points added from the mesh free method, have a pre-image point associated with it in the mesh. The current method does not. In the previous method, the boundary of a geometric object and its interior is defined by the points contained in a mesh that is created by the mesh free method known as the Reproducing Kernel Element Method (RKEM). The current application defines the extent of the body by the solvability of some mathematical equations known as the “consistency conditions” as represented by the “moment matrix.” Using the solvability criteria allows for the determination as to whether points are inside or outside the body without referring to any mesh at all. The present invention is the first to apply and exploit this definition to completely define an analytic geometry from an arbitrary point set.
Another method is disclosed by Lee et. al in “modeling and simulation of osteoporosis and frature of trabecular bone by meshless method.” Lee creates a meshless analysis-suitable geometry from CT scan data for trabecular bone, but several differences are important to note. First, Lee's method only works with structured, dense point sets, such as those coming from CT and Mill machines. The invention can use, but does not require such restrictions on input data. Note that it is well known in the community that structured dense points can easily be converted into an analysis-suitable geometry by creating a structured hexahedral mesh at each pixel in an individual slice, extending to the next slice. There are some nuances and choices to be made in that process, but they are not materially different from each other. Such models are called voxel models. Thus, Lee starts with a mesh and converts the voxels to meshfree particles. It is precisely this process the invention seeks to avoid, if desired, or required. Lee does down-sampling, as noted by “10×10×10 nodes, each corresponding to a set of 3×3×3 pixels,” but that is still constrained to be a structured dense set, and hence a voxel mesh, just coarser in resolution. The invention's approach to coarsening does not have that restriction. Further, in Equations 4 and 5 on p 333, Lee gives the boundary conditions for the loading of the model. To apply boundary conditions, which, by definition are on the surface of the model, Lee has to either use the surface of the underlying voxel mesh to apply boundary conditions, or assume the outer most particles are on the boundary. In the former case, Lee is relying on a mesh and his geometry is a hybrid of meshfree and mesh, with the interior volume represented by meshfree particles, and the boundary represented by the surface of the voxel model. It is worth noting that the surface of a voxel model is, in fact, a surface mesh. In the latter case, this is an assumption on the location of the boundary, which is not true, and is fundamental to the concept of the invention. Due to the non-local nature of meshfree shape functions, they will not be coincident with the locations of the boundary particles. Normally, meshfree basis functions do not have a precise boundary, as discussed above, but the invention provides a well-defined and computable boundary for meshfree modeling.
The present invention provides a new method based on a mesh free Galerkin formulation, in particular the Reproducing Kernel Particle Method (RKPM), to form an ASG of a discrete point set such as an anatomical structure. The use of the mesh free method known as the Reproducing Kernel Particle Method is incidental to the invention. Other mesh free methods, for example the Element Free Galerkin (EFG) method could be used equally as well.
In the mesh free method, no mesh is required for the analysis, and hence the troubles of meshing are avoided. Some implementations of mesh free methods still use a background mesh for integrating the weak form, but this mesh is not required to meet the more rigorous standards demanded by finite elements, and hence, can be generated fairly easily. The present method determines the particle distribution, particle interactions, support size, and representative volume associated with each particle.
Determining representative volume is simple if one has a mesh. In the case without a mesh, the trouble is that one does not know how to account for the overlap of support functions. In the present method, the over-all volume does not affect the solvability of the moment matrix, just the relative volume. This is only a problem near the boundary, where a method estimates the fraction of contribution of the window function volume to be used. Then, once the geometry is defined, the total volume is computed from the analysis-suitable representation and is used to scale all the relative volumes initially found.
An exemplary application of the present invention involves learning the mechanics of the pelvic floor. The female pelvic floor muscles form a complex structure responsible for supporting the pelvic organs such as rectum, vagina, bladder, and uterus. These muscles and associated connective tissues are ultimately anchored to the bony pelvic scaffold, and play a major additional role in maintaining continence of urine and bowel contents. Additionally, these muscles and associated connective tissues allow for important physiologic activities like urination, defecation, menstrual flow, and biomechanical processes like childbirth and sexual intercourse.
The major components of the pelvic floor are highlighted in FIG. 2(a) and FIG. 2(b). A thorough description of the functional anatomy of the female pelvic floor can be found in [Ashton-Miller and DeLancey (2007)], [Hoyte and Damaser (2007)] and [Herschorn (2004)]. The levator ani muscle group, as shown in FIG. 2(b) is the ultimate supporting structure responsible for holding organs in the body, and is rightfully the main focus of most studies regarding pelvic floor dysfunction [Hoyte, Schierlitz, Zou, Flesh, and Fielding (2001)], [Venugopala Rao, Rubod, Brieu, Bhatnagar, and Cosson (2010)], [Lien, Mooney, DeLancey, and Ashton-Miller (2004)]. The vagina, shown in FIG. 2(c), is suspended across the pelvis and is anchored in large part to the levator ani, and less so to the Obturator internus muscles. The vagina, in turn, supports the bladder and works with the levator ani to keep the rectum in a position appropriate for fecal continence at rest and bowel evacuation when appropriate.
Many finite element studies have been produced of the levator ani muscles ranging from shell element models to full volume element models [Hoyte, Damaser, Warfield, Chukkapalli, Majumdar, Choi, Trivedi, and Krysl (2008)], [Martins, Pato, Pires, Jorge, Parente, and Mascarenhas (2007)], [Noritomi, da Silva, Dellai, Fiorentino, Giorleo, and Ceretti (2013)]. These models have been valuable tools in learning about the mechanics of the pelvic floor, but many of the models focus solely on the levator ani, without considering the interaction between the other pelvic structures.
To help address this deficit, focus is placed on the vagina for the examples herein. Since a mesh is required for finite element analysis, the geometry is often idealized, both due to the piece-wise polyhedral approximation and the need to adjust the points to create a quality mesh. The goal was to accurately represent the geometry and produced studies involving multi-component interactions. In [Doblaré, Cueto, Calvo, Martinez, Garcia, and Cegoñino (2005)], the prospects of performing mesh-free analysis for biomechanics problems are discussed with several Galerkin methods being described. They chose to use the natural element method, which is closely tied to Voronoi diagrams, on the basis that essential boundary conditions are easily applied. The ease of applying the essential boundary conditions comes at the cost of generating a mesh of the domain, though the authors say the mesh generation requires no interaction with the user. They showed successful examples involving mostly bony tissue and some cartilage. Mesh-free methods have been used successfully in other areas of biomechanics including the heart [Liu and Shi (2003)], and the brain [Horton, Wittek, Joldes, and Miller (2010)], [Miller, Horton, Joldes, and Wittek (2012)]. In a similar vein, a hybrid mesh-free-mesh-based method based on the Reproducing Kernel Element Method (RKEM) was undertaken in [Simkins, Jr., Kumar, Collier, and Whitenack (2007) and Jr., Collier, Juha, and Whitenack (2008)]. RKEM details can be found in [Liu, Han, Lu, Li, and Cao (2004). Li, Lu, Han, Liu, and Simkins, Jr. (2004), Lu, Li, Simkins, Jr., Liu, and Cao (2004) and Simkins, Jr., Li, Lu, and Liu (2004)].
Accordingly, what is needed is an efficient mesh-free method for producing an ASG from a discrete point set. The automated analysis capability is demonstrated in modeling vaginal contracture, as might occur in cases of women treated with radiation for cervical cancer. However, in view of the art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill in the field of this invention how the shortcomings of the prior art could be overcome.
All referenced publications are incorporated herein by reference in their entirety. Furthermore, where a definition or use of a term in a reference, which is incorporated by reference herein, is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.
While certain aspects of conventional technologies have been discussed to facilitate disclosure of the invention, Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein.
The present invention may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that the invention may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the claimed invention should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.
In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned.